|
Mutually Exclusive
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both. In the coin-tossing example, both outcomes are, in theory, collectively exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6). Logic In logic, two propositions \phi and \psi are mutually exclusive if it is not logically possible for them to be true at the same time; that is, \lnot (\phi \land \psi) is a tautology. To say that more than two propositions are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Regression
In statistics, a logistic model (or logit model) is a statistical model that models the logit, log-odds of an event as a linear function (calculus), linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) estimation theory, estimates the parameters of a logistic model (the coefficients in the linear or non linear combinations). In binary logistic regression there is a single binary variable, binary dependent variable, coded by an indicator variable, where the two values are labeled "0" and "1", while the independent variables can each be a binary variable (two classes, coded by an indicator variable) or a continuous variable (any real value). The corresponding probability of the value labeled "1" can vary between 0 (certainly the value "0") and 1 (certainly the value "1"), hence the labeling; the function that converts log-odds to probability is the logistic function, hence the name. The unit of measurement for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mathematics
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship such objects have with physical reality consists. Major themes that are dealt with in philosophy of mathematics include: *''Reality'': The question is whether mathematics is a pure product of human mind or whether it has some reality by itself. *''Logic and rigor'' *''Relationship with physical reality'' *''Relationship with science'' *''Relationship with applications'' *''Mathematical truth'' *''Nature as human activity'' (science, the arts, art, game, or all together) Major themes Reality Logic and rigor Mathematical reasoning requires Mathematical rigor, rigor. This means that the definitions must be absolutely unambiguous and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MECE Principle
The MECE principle (mutually exclusive and collectively exhaustive) is a grouping principle for separating a set of items into subsets that are mutually exclusive (ME) and collectively exhaustive (CE). It was developed in the late 1960s by Barbara Minto at McKinsey & Company and underlies her Minto Pyramid Principle, and while she takes credit for MECE, according to her interview with McKinsey, she says the idea for MECE goes back as far as to Aristotle. The MECE principle has been used in the business mapping process wherein the optimum arrangement of information is exhaustive and does not double count at any level of the hierarchy. Examples of MECE arrangements include categorizing people by year of birth (assuming all years are known), apartments by their building number, letters by postmark, and dice rolls. A non-MECE example would be categorization by nationality, because nationalities are neither mutually exclusive (some people have dual nationality) nor collectively exha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchronicity
Synchronicity () is a concept introduced by Carl Jung, founder of analytical psychology, to describe events that coincide in time and appear meaningfully related, yet lack a discoverable causal connection. Jung held that this was a healthy function of the mind, although it can become harmful within psychosis. Jung developed the theory as a hypothetical noncausal principle serving as the intersubjective or philosophically objective connection between these seemingly meaningful coincidences. After coining the term in the late 1920s Jung developed the concept with physicist Wolfgang Pauli through correspondence and in their 1952 work ''The Interpretation of Nature and the Psyche''. This culminated in the Pauli–Jung conjecture.Jung, Carl G. 9512005.Synchronicity. Pp. 91–98 in ''Jung on Synchronicity and the Paranormal'', edited by R. Main. London: Taylor & Francis. Jung and Pauli's view was that, just as causal connections can provide a meaningful understanding of the psyc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxymoron
An oxymoron (plurals: oxymorons and oxymora) is a figure of speech that Juxtaposition, juxtaposes concepts with opposite meanings within a word or in a phrase that is a self-contradiction (other), self-contradiction. As a rhetorical device, an oxymoron illustrates a point to communicate and reveal a paradox. A general meaning of "contradiction in terms" is recorded by the 1902 edition of the ''Oxford English Dictionary. The term ''oxymoron'' is first recorded as Latinized Greek ', in Maurus Servius Honoratus (c. AD 400); it is derived from the Ancient Greek, Greek word ' "sharp, keen, pointed" Retrieved 26 February 2013. and "dull, stupid, foolish"; as it were, "sharp-dull", "keenly stupid", or "pointedly foolish".. Retrieved 26 February 2013. "Pointedly foolish: a witty saying, the more pointed from being paradoxical or seemingly absurd." The word ''oxymoron'' is autological, i.e., it is itself an example of an oxymoron. The Greek compound word ', which would corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event Structure
Event may refer to: Gatherings of people * Ceremony, an event of ritual significance, performed on a special occasion * Convention (meeting), a gathering of individuals engaged in some common interest * Event management, the organization of events * Festival, an event that celebrates some unique aspect of a community * Happening, a type of artistic performance * Media event, an event created for publicity * Party, a social, recreational or corporate events held * Sporting event, at which athletic competition takes place * Virtual event, a gathering of individuals within a virtual environment Science, technology, and mathematics * Event (computing), a software message indicating that something has happened, such as a keystroke or mouse click * Event (philosophy), an object in time, or an instantiation of a property in an object * Event (probability theory), a set of outcomes to which a probability is assigned * Event (relativity), a point in space at an instant in time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Bind
A double bind is a dilemma in communication in which an individual (or group) receives two or more mutually conflicting messages. In some scenarios (such as within families or romantic relationships), this can be emotionally distressing, creating a situation in which a successful response to one message results in a failed response to the other (and vice versa), such that the person responding will automatically be perceived as in the wrong, no matter how they respond. Double bind theory was first stated by Gregory Bateson and his colleagues in the 1950s,Bateson, G., Jackson, D. D., Haley, J. & Weakland, J., 1956, Toward a theory of schizophrenia.''Behavioral Science'', Vol. 1, 251–264. in a theory on the origins of schizophrenia and post-traumatic stress disorder. It was theorized that schizophrenic responses were a reaction to an individual facing a competing demands, leaving them with no clear way of responding. Double binds are often utilized as a form of control withou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disjoint Sets
In set theory in mathematics and Logic#Formal logic, formal logic, two Set (mathematics), sets are said to be disjoint sets if they have no element (mathematics), element in common. Equivalently, two disjoint sets are sets whose intersection (set theory), intersection is the empty set.. For example, and are ''disjoint sets,'' while and are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint. Generalizations This definition of disjoint sets can be extended to family of sets, families of sets and to indexed family, indexed families of sets. By definition, a collection of sets is called a ''family of sets'' (such as the power set, for example). In some sources this is a set of sets, while other sources allow it to be a multiset of sets, with some sets repeated. An \left(A_i\right)_, is by definition a set-valued Function (mathematics), function (that is, it is a function that assigns a set A_i to every ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomy
A dichotomy () is a partition of a set, partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are Complement (set theory), complements. In logic, the partitions are dual (category theory), opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multicategorical variables as binary variables is called discretization, dichotomization. The discretization error inherent in dichoto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contrariety
In lexical semantics, opposites are words lying in an inherently incompatible binary relationship. For example, something that is ''even'' entails that it is not ''odd''. It is referred to as a 'binary' relationship because there are two members in a set of opposites. The relationship between opposites is known as opposition. A member of a pair of opposites can generally be determined by the question: "What is the opposite of ''X''" The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are word pairs whose meanings are opposite and which lie on a continuous spectrum (''hot'', ''cold''). Complementary antonyms are word pairs whose meanings are opposite but whose meanings do not lie on a continuous spectrum (''push'', ''pull''). Relational antonyms are word pairs where opposite makes sense only in the context of the relationship between the two meanings (''teach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
